A test for robustness in harvest scheduling models

A test for robustness in harvest scheduling models
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  A test for robustness in harvest scheduling models M. Boyland a, *, J. Nelson b , F.L. Bunnell a a  Department of Forest Sciences, Faculty of Forestry, University of British Columbia,#3041–2424 Main Mall, Vancouver, BC, Canada V6T 1Z4 b  Department of Forest Resource Management, Faculty of Forestry, University of British Columbia,#3041–2424 Main Mall, Vancouver, BC, Canada V6T 1Z4 Abstract Harvest scheduling models are decision support systems used to project sustainable harvest volumes while maintainingsocial and ecological objectives. We present a robustness test for these projections that measure the possible level of deviationbetween projection and implementation while still meeting projected target levels. Results using both simulation andoptimization models indicate that when using a maximum sustainable volume objective, the projections have very littlerobustness. Reducing the target volume increases robustness, but with a large cost to the sustainable timber harvest level.Matching the level of uncertainty in the planning environment with corresponding level of robustness in projections is animportant factor in creating sustainable forest management plans. # 2004 Elsevier B.V. All rights reserved. Keywords:  Harvest scheduling; Forest management; Robust; Uncertainty 1. Introduction The predominant conflict in many forests isbetween timber harvesting and retaining forest landsfor ecological and social objectives. Decision SupportSystems (DSS) such as harvest scheduling models areused to help explore and balance these objectives.These harvest schedulers forecast future forestinventories and harvest volumes produced by aschedule of projected harvest entries. Within astrategic planning context, the scheduled planninghorizon can extend from 100 years to a few harvestrotations. Even with the same Annual Allowable Cut(AAC), changing the order of harvest entries canchange the efficiency and economics of production byharvesting stands at different ages and locations. Thisis exploited by harvest schedulers that use optimiza-tion to find clever combinations of harvest entries tomaximize outputs (Lockwood and Moore, 1993;Crowe et al., 2003).A critical assumption in these models is that theprojected harvest schedule is representative of theharvest schedule that will be eventually implemented.The exact implementation of the harvest schedule isnot necessarily required, because many closely relatedschedules often can achieve the same objectives.However, factors such as changing environmental Ecology and Management 207 (2005) 121–132* Corresponding author. Tel.: +1 604 822 6592. E-mail address: (M. Boyland).0378-1127/$ – see front matter # 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.foreco.2004.10.022  regulations, social objectives (Cerda, 2002), andnatural disturbances (Klenner et al., 2000), create uncertainty in harvest scheduling even in the shortterm, and can be considerable over the long term.These uncertainties drive changes in the implementa-tion of harvest schedules, which, if large enough,result in lower outputs than the forecasted objectivelevels. Changes to the harvest schedule are also madeas a reaction to changing markets and price  fl uctua-tions. Whether as a reaction to new regulations or adesire to exploit a new market, retaining the  fl exibilityto respond to changing conditions requires that theAAC be set at a level that allows for implementationchange while maintaining sustainable economic andecological objectives.The level of change between harvest plans andimplemented harvest location has been measured for alandscape unit in British Columbia. Cerda (2002)found that only1 ha inevery8.3 ha proposed in 5-yearharvest plan was actuallycut. Differences were causedby changes in social constraints, economic andoperational constraints, natural disturbances, andnew wildlife requirements. A 7.3:1 ratio of plannedhectares to harvested hectares translates into an 86%difference between the proposed and implementedharvest schedules. This is likely an extreme case for a5-year tactical plan. However, over the longer term,high uncertainty is more likely. Harvesting in thePaci fi c Northwest has rapidly moved from progressiveclearcutting, to a three-pass system where largecutblocks are created through three separate entries,to small clearcuts with adjacency constraints, and nowin some areas is changing to selection systems withvariable retention harvesting (Beese et al., 2001). Thistype of progression creates a highly uncertainplanning environment, and requires a correspondinglyrobust strategic plan with the  fl exibility to incorporatechange.Testing robustness adds a second dimension tomeasuring the sustainability of an AAC. TraditionalDSS ’ s project a harvest schedule to demonstrate thatan AAC can be met. The robustness test presented inthis paper supplements this by demonstrating that theAAC can be met after a wide variety of changes havebeen made to the harvest schedule. Robustness testingalsorevealswhichmodelstructuresareappropriatefordifferent uncertainty levels.Highlyuncertain planningenvironmentswillrequiredifferenttoolswithdifferentcapabilities than environments with more securefutures (Courtney et al., 1997). When uncertainty is low, implementation is less likely to signi fi cantlydiverge from the projected schedules, and the risk of failing to sustain objective levels is low. Lowuncertainty in the planning environment can beexploited with optimization harvest schedulers thatincrease objective levels through specialized sche-dules. High uncertainty should be matched withmodels that create robust projections, perhaps inconjunction with a reduced harvest level.DSS ’ s for controlling harvest volume and environ-mental objectives have evolved into two majorcategories: simulators and optimizers. Models thatincorporate spatial objectives such as patch-sizepattern and reserves now dominate both categories.Simulators predict the consequences of harvest policyonsustainablevolumeandlandscapeattributessuchasseral-patch distribution (Bunnell et al., 1999; Nelsonand Wells, 2000) and landscape structure (Gustafsonand Crow, 1996). They often are used to projectsustainable AAC ’ s and the state of the forest given aset of constraints and simple harvest rules (Carter etal., 1997).Optimization models  fi nd the combination of management actions that produce the best objectivelevels.  ‘‘ Best ’’  is usually de fi ned in terms of highestvolume or most pro fi t, and often in combination withecological indicators such as seral constraints, patchsizes, and habitat goals (Hof and Joyce, 1993;Bettinger et al., 1997; Liu et al., 2000) or othereconomicindicatorssuchasroadaccess(RichardsandGunn, 2000). Many optimizing methods exist, thoughnot all of them guarantee optimal schedules. Integerprogramming (IP) models do  fi nd optimal solutions,but are limited to small problems (McDill et al., 2002;Crowe et al., 2003). Heuristics are used in situationswhere IP solutions are impractical, and often producesolutions close to optimal (Boston and Bettinger,1999; Bettinger et al., 2002). Many have beenemployed such as Simulated Annealing (Lockwoodand Moore, 1993; Chen and Gadow, 2002), Geneticalgorithms (Mullen and Butler, 1997; Bettinger et al.,2002), Tabu search (Murray and Church, 1995), and Hill climbing (Crowe, 2001).The split between simulator and optimizer isrelevant to uncertainty because of the explicit attemptin optimizers to produce the  ‘‘ best ’’  solution. Where  M. Boyland et al./Forest Ecology and Management 207 (2005) 121  –  132 122  the single, optimal schedule is produced, it is possiblethat any implementation change will result in anegative impact on objectives. Simulators rely onharvest rules to project AAC ’ s, making no concertedeffort at optimality, and therefore may be able tocapitalize on mediocre schedules through increased fl exibility during implementation.Theobjectiveofthispaperistoassesstherobustnessof harvest scheduling decision support systems underdifferent levels of uncertainty in the planning environ-ment. Two types of harvest scheduling DSS ’ s,simulatorsandoptimisers,areexaminedfortheirabilityto respond to changes between the projected and theimplementedharvestschedules.Weexaminechangesinthe order of harvest, measuring how many changes canbe made from the projected harvest schedule before itfails to achieve objective targets.We continue with a methods section outlining aproblem de fi nition of the planning environment anddescriptions of a simulation model and heuristicoptimization model, as well as a description of thesample landbase. An explanation is then provided forthe tests of robustness applied on the sample land-scape. The results are then presented and discussed.The paper  fi nishes with conclusions and recommen-dations for further research. 2. Methods and material 2.1. Harvest scheduler problem definition DSS ’ s are most effectively used when explicitquestions are posed (Bunnell and Boyland, 2002). The basic question asked here is:  ‘‘ What sustainable levelof harvest can also maintain the seral targets? ’’  Theharvest objective is a surrogate for economic goals(pro fi t) as well as social goals (employment, com-munity stability). Seral constraints control the age – class structure of the forest and are surrogates for awiderange ofgoalsinvolvingforest health, recreation,viewsheds, and drinking water.The seral classes are de fi ned by age – class rangesset to coincide with the appearance of stand structureattributes (Table 1). Old and mature seral stands arerequired on a minimum percentage of the landbase,while a young seral stand is limited to a maximumpercentage of the landbase. In addition, constraints areapplied for minimum rotation age, adjacency, andeven- fl ow. For each stand group, a minimum rotationageissettopreventharvestifanypolygonisbelowtheminimum rotation age. The adjacency constraint is 10years for all stand types, preventing the harvest of anyharvest unit sharing a boundary with any polygon lessthan 10-years old. The harvest options are to clearcut,or to do nothing. The planning horizon is set to 100years. 2.1.1. Simulation model: SimSched  The simulation model presented here is similar tothat of  Nelson (2003), following the Unit Restricted Model formulation (Murray, 1999). SimSched har- vests prede fi ned harvest units subject to adjacency,rotation age, and volume regulation constraints. Theseare applied as hard constraints, with no harvestingallowed if any constraint drops below its targetedlevel.Simulations start at year 0, and sequentiallyprogress through each year (Fig. 1a). Each yearbegins by calculating the seral stage distribution, andcreating a harvest queue. SimSched uses an oldest  fi rstalgorithm that ranks harvest units based on their agefrom oldest to youngest. The model selects from theharvest queue, subject to constraints, until the yearlyvolume target is satis fi ed or the harvest queue isexhausted. The maximum AAC ’ s are found byiteratively raising and lowering the harvest target(to the nearest 1000 m 3 ).  M. Boyland et al./Forest Ecology and Management 207 (2005) 121–132  123Table 1Seral class de fi nitionsSeral class name Stand attributes Landscape target (%) Kootenay conditions (%)Old Heterogeneous canopy structure, decaying largesnags and coarse woody debris > 12 19.5Mature Large live trees, shrubs, large snags  > 30 44.4Young Fully stocked stand, canopy closure  < 33 17.1  2.2. Heuristic optimizing model: OptSched  The optimization model, OptSched, uses thesimulated annealing algorithm similar to Lockwoodand Moore (1993) and Liu et al. (2000). As in SimSched, the Unit Restricted Model is used. Thesimulated annealing algorithm does not  fi nd exactoptimal solutions, but it is a good alternative whereproblem size makes exact methods infeasible (Bet-tinger et al., 2002).Optimality is scored based on a penalty weightingsystem for each objective, with an objective function  M. Boyland et al./Forest Ecology and Management 207 (2005) 121  –  132 124Fig. 1. Overview of model procedures for (a) SimSched and (b) OptSched.  that sums each penalty score into a single value (Eq.(1)). In a heuristic model, completely excludinginfeasible solutions can adversely affect the searchprocess. Instead, OptSched applies penalties tosituations where objectives are not met. Penaltiesaccrue from the difference between the target andachieved level for each objective, multiplied by apenalty weight (Fig. 2). The shape of individualpenalty functions was created by considering  fi rst, theintent of the penalty, and second, through an iterativeprocess that improved algorithm behaviour ( fi nalscore level and score trajectory through time). Largerpenalty weights encourage the algorithm to resolvethese objective penalties  fi rst. Individual penaltyweights were calculated through an ordered searchof parameters considered plausible, with the bestperformingparameterschosen.BecauseOptSchedcanproduce solutions that violate the minimum objectivelevels, solutions were checked for such violationsbefore accepted as valid.OptSched attempts to minimize the sum of allpenalties through a series of random moves (Fig. 1b).The notation for the model is presented below:  Z   = total penalty score;  p ij  = penalty associated with year  i , and objective  j .  I   = length of the planning horizon (years). Q  = number of polygons in the landbase. QA q  = number of polygons adjacent to polygon  q .aa q  = minimum adjacency age of polygon  q  (years). h qi  = 1 if polygon  q  is harvested in year  i ; 0 otherwise. s q  = area of polygon  q  (ha).ra q  = rotation age of polygon  q  (years). a qi  = age of polygon  q  in year  i  (years).  M. Boyland et al./Forest Ecology and Management 207 (2005) 121  –  132  125Fig. 2. Penalty functions for the OptSched model.
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